TY - JOUR
T1 - Unitarity of generalized fourier-gauss transforms
AU - Ji, Un Cig
AU - Obata, Nobuaki
N1 - Funding Information:
This study was supported by Grant No. R05-2002-000-00142-0 from the Basic Research Program of the Korea Science & Engineering Foundation, by Grant-in-Aid for Scientific Research No. 15340039 of JSPS and by the program “R & D Support Scheme for Funding Selected IT Proposals" of the Ministry of Public Management, Home Affairs, Posts and Telecommunications.
PY - 2006/8/1
Y1 - 2006/8/1
N2 - A generalized Fourier-Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.
AB - A generalized Fourier-Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.
KW - Boson Fock space
KW - Fourier-Gauss transform
KW - Generalized dilation
KW - Generalized Fourier-Gauss transform
KW - Kuo's Fourier transform
KW - Unitarity
KW - White noise theory
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U2 - 10.1080/07362990600751837
DO - 10.1080/07362990600751837
M3 - Article
AN - SCOPUS:33745844408
SN - 0736-2994
VL - 24
SP - 733
EP - 751
JO - Stochastic Analysis and Applications
JF - Stochastic Analysis and Applications
IS - 4
ER -